改进的基于弹性核法的曲梁有限梁段法  

IMPROVEMENT ABOUT FINITE SEGMENT ELEMENT METHOD OF CURVED GIRDER BASED ON THEORY OF SPRING-CENTER METHOD

作　　者：宋郁民[1] 吴定俊[1] 

机构地区：[1]同济大学桥梁工程系,上海200092

出　　处：《工程力学》2011年第A01期16-21,共6页Engineering Mechanics

摘　　要：基于弹性核法的曲梁有限梁段法,在求解曲梁单元刚度矩阵时,因柔度矩阵的表达式繁琐,难以直接求逆得到单元刚度矩阵的解析表达式。相关文献及曲梁的梁段有限元程序均采用数值方法求逆,得其刚度矩阵。该文提出一个矩阵求逆理论,并证明之。依此理论推导出曲梁单元刚度矩阵的解析解,并提出对曲梁有限梁段法的改进。算例验证了公式的正确性和可靠性。依据改进后的曲梁单元刚度矩阵及其解析解,简化了曲梁杆系结构有限元程序的编制,提高了微机工作效率和计算精度。Based on the spring-center method of a curved-girder-finite-segment-element method,the flexibility matrix is deduced,but it is difficult to solve its inverse matrix directly and get an analytical solution of a stiffness matrix because each element is very complex.The numerical method is used to solve an inverse matrix in related documents and finite element program usually.In this paper,a method of matrix inversion is proposed and verified,and the concrete expression of the stiffness matrix is gotten according to the method of matrix inversion,and the improvement of a curved-girder-finite-segment-element method is proposed.The example and comparison indicate the method and formulas are correct and reliable.On the basis of the new method and analytical solution of the stiffness matrix,the program of the curved-girder-finite-segment-element method is simplified greatly,and efficiency and accuracy of a computer are improved.

关 键 词：桥梁工程 曲线桥梁 有限梁段法 曲梁单元 弹性核法 柔度矩阵 刚度矩阵 计算效率和精度 

分 类 号：U448.42[建筑科学—桥梁与隧道工程] TB115[交通运输工程—道路与铁道工程]